23 citations · 56 across the 8 of their papers we have counts for
8 papers
A fast two-level Strang splitting method for multi-dimensional spatial fractional Allen-Cahn equations with discrete maximum principle
Yao-Yuan Cai, Zhi-Wei Fang, Hao Chen +1
In this paper, we study the numerical solutions of the multi-dimensional spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivat…
Robust fast method for variable-order time-fractional diffusion equations without regularity assumptions
Jia-Li Zhang, Zhi-Wei Fang, Hai-Wei Sun
In this paper, we develop a robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion equations (tFDEs), superiorly handling the cases of small or vanish…
A preconditioner based on sine transform for two-dimensional Riesz space factional diffusion equations in convex domains
Xin Huang, Hai-Wei Sun
In this paper, we develop a fast numerical method for solving the time-dependent Riesz space fractional diffusion equations with a nonlinear source term in the convex domain. An im…
Fast second-order evaluation for variable-order Caputo fractional derivative with applications to fractional sub-diffusion equations
Jia-li Zhang, Zhi-wei Fang, Hai-wei Sun
In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on - formula and the exponent…
Spectral analysis for preconditioning of multi-dimensional Riesz fractional diffusion equations
Xin Huang, Xue-Lei Lin, Michael K. Ng +1
In this paper, we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion equations. The finite difference…
Exponential-sum-approximation technique for variable-order time-fractional diffusion equations
Jia-Li Zhang, Zhi-Wei Fang, Hai-Wei Sun
In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function , we develop an exponential-sum-approximation (ESA) technique t…
Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian
Xian-Ming Gu, Hai-Wei Sun, Yanzhi Zhang +1
In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplac…
An efficient second-order convergent scheme for one-side space fractional diffusion equations with variable coefficients
Xue-lei Lin, Pin Lyu, Michael K. Ng +2
In this paper, a second order finite difference scheme is investigated for time-dependent one-side space fractional diffusion equations with variable coefficients. The existing sch…